Sphere packings II
Metric Geometry
2007-05-23 v1
Abstract
An earlier paper describes a program to prove the Kepler conjecture on sphere packings. This paper carries out the second step of that program. A sphere packing leads to a decomposition of into polyhedra. The polyhedra are divided into two classes. The first class of polyhedra, called quasi-regular tetrahedra, have density at most that of a regular tetrahedron. The polyhedra in the remaining class have density at most that of a regular octahedron (about 0.7209).
Cite
@article{arxiv.math/9811074,
title = {Sphere packings II},
author = {Thomas C. Hales},
journal= {arXiv preprint arXiv:math/9811074},
year = {2007}
}
Comments
18 pages. Second of two older papers in the series on the proof of the Kepler conjecture. See math.MG/9811071. The original abstract is preserved